284-286] RELATIVITY OF FORCE. 361 



*286. Choice of Origin. In choosing the origin of a frame 

 of reference for the motion of any system of bodies, it is in the 

 first place necessary to observe that the Postulates of Mechanics 

 (Article 87) will in general be inapplicable if the origin is taken 

 at the position of any definite particle of the system. For, if 

 this were done, that particle would have no motion, and could 

 not be subject to any resultant force. Now the masses of parts 

 of a system are determined by observing the ratios of their 

 accelerations relative to a properly chosen frame, and to secure 

 that any part shall always have zero acceleration we should 

 have to take the mass of that part to be infinite, and then no 

 definite number however great could represent this mass. It 

 is one of our Postulates that every body and every part of a 

 body has a definite mass, and it thus appears that this Postulate 

 implies a restriction upon the position of the origin of the frame 

 of reference ; it may not be taken at the position of one of the 

 particles. 



To take an example : In discussing the motions of bodies 

 relative to the Earth, the Postulates do not apply if the origin 

 is taken at the centre of the Earth, unless the mass of the Earth 

 is taken to be infinite. The mass of the Earth is, however, 

 assumed to be a determinate multiple of the mass of any par- 

 ticular body, and this multiple can be determined in accordance 

 with the Law of Gravitation. In general, it appears that the 

 postulates cannot be applied without error to the motion of a 

 body if the origin of the frame of reference is fixed relatively 

 to the Earth, and the error that would arise in such an application 

 consists in the neglect of the fraction (mass of body : mass of 

 Earth). In Articles 278 to 284 this fraction is neglected. 



Again, we have said that the interaction between two particles 

 consists of two equal and opposite forces in the line joining them, 

 the force on one particle being measured by the product of the 

 mass of that particle and a component of its acceleration, and 

 we have seen how the theory of the motion of the centre of 

 inertia enables us to replace a body by a certain particle. Now, 

 if in a system of two bodies with relative accelerations we took 

 the origin of a frame of reference at the centre of inertia of one 

 body, then the magnitude of the force exerted by the second 

 body upon the first would be zero, and accordingly the first 



